An Optimal Dimensionality Sampling Scheme on the Sphere for Antipodal Signals In Diffusion Magnetic Resonance Imaging

We propose a sampling scheme on the sphere and develop a corresponding spherical harmonic transform (SHT) for the accurate reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal symmetry, we design a sampling scheme that requires the optimal number of samples on the sphere, equal to the degrees of freedom required to represent the antipodally symmetric band-limited diffusion signal in the spectral (spherical harmonic) domain. Compared with existing sampling schemes on the sphere that allow for the accurate reconstruction of the diffusion signal, the proposed sampling scheme reduces the number of samples required by a factor of two or more. We analyse the numerical accuracy of the proposed SHT and show through experiments that the proposed sampling allows for the accurate and rotationally invariant computation of the SHT to near machine precision accuracy.Comment: Will be published in the proceedings of the International Conference Acoustics, Speech and Signal Processing 2015 (ICASSP'2015

Gaussian process regression can turn non-uniform and undersampled diffusion MRI data into diffusion spectrum imaging

We propose to use Gaussian process regression to accurately estimate the diffusion MRI signal at arbitrary locations in q-space. By estimating the signal on a grid, we can do synthetic diffusion spectrum imaging: reconstructing the ensemble averaged propagator (EAP) by an inverse Fourier transform. We also propose an alternative reconstruction method guaranteeing a nonnegative EAP that integrates to unity. The reconstruction is validated on data simulated from two Gaussians at various crossing angles. Moreover, we demonstrate on non-uniformly sampled in vivo data that the method is far superior to linear interpolation, and allows a drastic undersampling of the data with only a minor loss of accuracy. We envision the method as a potential replacement for standard diffusion spectrum imaging, in particular when acquistion time is limited.Comment: 5 page

Diffusion sampling schemes: A generalized methodology with nongeometric criteria

Producción CientíficaPurpose:The aim of this paper is to show that geometrical criteria for designingmultishellq-space sampling procedures do not necessarily translate into recon-struction matrices with high figures of merit commonly used in the compressedsensing theory. In addition, we show that a well-known method for visitingk-space in radial three-dimensional acquisitions, namely, the Spiral Phyllotaxis,is a competitive initialization for the optimization of our nonconvex objectivefunction.Theory and Methods:We propose the gradient design method WISH (WeIght-ing SHells) which uses an objective function that accounts for weighted dis-tances between gradients withinM-tuples of consecutive shells, withMrangingbetween 1 and the maximum number of shellsS. All theM-tuples share thesame weight�M. The objective function is optimized for a sample of theseweights, using Spiral Phyllotaxis as initialization. State-of-the-art General Elec-trostatic Energy Minimization (GEEM) and Spherical Codes (SC) were used forcomparison. For the three methods, reconstruction matrices of the attenuationsignal using MAP-MRI were tested using figures of merit borrowed from theCompressed Sensing theory (namely, Restricted Isometry Property —RIP— andCoherence); we also tested the gradient design using a geometric criterion basedon Voronoi cells.Results:For RIP and Coherence, WISH got better results in at least one com-bination of weights, whilst the criterion based on Voronoi cells showed anunrelated pattern.Conclusion:The versatility provided by WISH is supported by better results.Optimization in the weight parameter space is likely to provide additionalimprovements. For a practical design with an intermediate number of gradients,our results recommend to carry out the methodology here used to determine theappropriate gradient table.Agencia Estatal de Investigación,(under Grants RTI2018-094569-B-I00,PID2020-115339RB-I00 and TED2021-130090B-I00)ESAOTE, Ltd (Grant/Award Number: 18IQBM

Design of multishell sampling schemes with uniform coverage in diffusion MRI

International audiencePURPOSE: In diffusion MRI, a technique known as diffusion spectrum imaging reconstructs the propagator with a discrete Fourier transform, from a Cartesian sampling of the diffusion signal. Alternatively, it is possible to directly reconstruct the orientation distribution function in q-ball imaging, providing so-called high angular resolution diffusion imaging. In between these two techniques, acquisitions on several spheres in q-space offer an interesting trade-off between the angular resolution and the radial information gathered in diffusion MRI. A careful design is central in the success of multishell acquisition and reconstruction techniques. METHODS: The design of acquisition in multishell is still an open and active field of research, however. In this work, we provide a general method to design multishell acquisition with uniform angular coverage. This method is based on a generalization of electrostatic repulsion to multishell. RESULTS: We evaluate the impact of our method using simulations, on the angular resolution in one and two bundles of fiber configurations. Compared to more commonly used radial sampling, we show that our method improves the angular resolution, as well as fiber crossing discrimination. DISCUSSION: We propose a novel method to design sampling schemes with optimal angular coverage and show the positive impact on angular resolution in diffusion MRI

Predictive Diagnosis of Alzheimer's Disease using Diffusion MRI

Age-related neurodegenerative diseases, including Alzheimer’s Disease (AD), are an increasing cause of concern for the world’s ageing population. The current consensus in the research community is that the main setbacks in the treatment of AD include the inability to diagnose it in its early stages and the lack of accurate stratification techniques for the prodromal stages of the disease and normal control (NC) subject groups. Numerous studies show that AD causes damage to the white matter microstructure in the brain. Commonly used techniques for diagnosing this disease include, neuropsychological assessments, genetics, proteomics, and image-based analysis. However, unlike these techniques, recent advances in Diffusion Magnetic Resonance Imaging (dMRI) analysis posits its sensitivity to the microstructural organization of cerebral white matter, and hence its applicability for early diagnosis of AD. Since tissue damage is reflected in the pattern of water diffusion in neural fibre structures, dMRI can be used to track disease-related changes in the brain. Contemporary dMRI approaches are broadly classified as being either region-based or tract-based. This thesis draws on the strengths of both these approaches by proposing an original extension of region-based methods to the simultaneous analysis of multiple brain regions. A predefined set of features is derived from dMRI data and used to compute the probabilistic distances between different brain regions. The resulting statistical associations can be modelled as an undirected and fully-connected graph encoding a unique brain connectivity pattern. Subsequently, the characteristics of this graph are used for the stratification of AD and NC subjects. Although the current work focuses on AD and NC subject populations, the perfect separability achieved between the two groups suggests the suitability of the technique for separating NC, AD, in addition to subjects in the prodromal stage of the disease, i.e., mild cognitive impairment (MCI)

Super Resolution of HARDI images Using Compressed Sensing Techniques

Effective techniques of inferring the condition of neural tracts in the brain is invaluable for clinicians and researchers towards investigation of neurological disorders in patients. It was not until the advent of diffusion Magnetic Resonance Imaging (dMRI), a noninvasive imaging method used to detect the diffusion of water molecules, that scientists have been able to assess the characteristics of cerebral diffusion in vivo. Among different dMRI methods, High Angular Resolution Diffusion Imaging (HARDI) is well known for striking a balance between ability to distinguish crossing neural fibre tracts while requiring a modest number of diffusion measurements (which is directly related to acquisition time). HARDI data provides insight into the directional properties of water diffusion in cerebral matter as a function of spatial coordinates. Ideally, one would be interested in having this information available at fine spatial resolution while minimizing the probing along different spatial orientations (so as to minimize the acquisition time). Unfortunately, availability of such datasets in reasonable acquisition times are hindered by limitations in current hardware and scanner protocols. On the other hand, post processing techniques prove promising in increasing the effective spatial resolution, allowing more detailed depictions of cerebral matter, while keeping the number of diffusion measurements within a feasible range. In light of the preceding developments, the main purpose of this research is to look into super resolution of HARDI data, using the modern theory of compressed sensing. The method proposed in this thesis allows an accurate approximation of HARDI signals at a higher spatial resolution compared to data obtained with a typical scanner. At the same time, ideas for reducing the number of diffusion measurements in the angular domain to improve the acquisition time are explored. Accordingly, the novel method of applying two distinct compressed sensing approaches in both spatial and angular domain, and combining them into a single framework for performing super resolution forms the main contribution provided by this thesis

The analysis and application of dynamic MRI contrasts to grape berry biology

Magnetic resonance imaging (MRI) is a powerful, non-invasive imaging tool. When MRI is employed in the study biological systems, the acquired images reflect different aspects of system morphology and/or physiology. This thesis explores the application of relaxation and diffusion MRI to the study of different biological aspects of the fruit of the common grape vine, Vitis vinifera L., a highly valued botanical species. The results of this investigation have put forth a number of contributions to this area of research. The studies within this thesis began with a necessary validation for the application of diffusion MRI techniques to the grape berry using simulated cellular geometries to determine how broad plant cells could potentially influence the accurate reconstruction of the grape berry morphology. The result of this validation will also prove useful for other wide geometry applications wider than 10 μm. Relaxation and diffusion MRI was also used to study changes to berry morphology resulting from berry development and ripening. This study provided a novel perspective on grape berry development and demonstrated that diffusion anisotropy patterns correlated with the microstructure of the major pericarp tissues of grape berries, including the exocarp, outer and inner mesocarp, seed interior, as well as microstructural variations across grape berry development. This study also provided further evidence that the inner mesocarp striation patterns observed in the spin-spin relaxation weighted images of previous studies arise due to variations in cell width across the striation bands. Diffusion MRI was employed to investigate the morphological and physiological changes to occur within grape berries during fruit split, a costly source of fruit loss in vineyards. This study revealed water uptake through splits in the berry epidermis will result in the loss of parenchyma cell vitality about these wounds. The amount of water left standing on the surface of split grape berries may hence be an important determinant of the cellular response of the fruit to this trauma, and the subsequent establishment of adventitious fruit pathogens. Additionally, paramagnetically enhanced spin-lattice relaxation MRI was used to undertake a novel examination of the diffusive transport of manganese across the berry pericarp. The results of this study shows that the transport of manganese is within the berry xylem influences manganese exiting of ‘downstream’ of the pedicel, and that cellular membranes affect the spatial distribution of manganese across the berry pericarp. Manganese proved to be an excellent tracer for these experiments, and future investigations making use of paramagnetically enhanced relaxation MRI, perhaps employing other paramagnetic materials such as iron or copper, could prove to be valuable in determining how botanical species transport and store these materials within sink organs